The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates

Abstract

Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized -in a static environment under mass-conservation and enzyme expression constraints-we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space. Author summaryThe microbial genome encodes for a large network of enzyme-catalyzed reactions. The reaction rates depend on concentrations of enzymes and metabolites, which in turn depend on those rates. Cells face a number of biophysical constraints on enzyme expression, for example due to a limited membrane area or cytosolic volume. Considering this complexity and nonlinearity of metabolism, how is it possible, that experimental data can often be described by simple linear models? We show that it is evolution itself that selects for simplicity. When reproductive rate is maximised, the number of active independent metabolic pathways is bounded by the number of growth-limiting enzyme constraints, which is typically small. A small number of pathways automatically generates the measured simple relations. We identify the December 21, 2018 1/25 importance of growth-limiting constraints in shaping microbial behaviour, by focussing on their mechanistic nature. We demonstrate that overflow metabolism -an important phenomenon in bacteria, yeasts, and cancer cells -is caused by two constraints on enzyme expression. We derive experimental guidelines for constraint identification in microorganisms. Knowing these constraints leads to increased understanding of metabolism, and thereby to better predictions and more effective manipulations. 25 We found an evolutionary extremum principle: growth-rate maximization driv...

Elementary Growth Modes provide a molecular description of cellular self-fabrication

“…Given that the constant osmotic pressure constraint was already active, the number of active EGMs is thus bounded by the number of constraints on enzyme expression. We hereby generalized yet another existing result for EFMs to their self-fabricating counterparts (de Groot et al, 2019).…”

“…Proof. Let us consider the maximisation problem for an arbitrary fixed set of metabolite concentrations x (inspired by the proofs from (Wortel et al, 2014;de Groot et al, 2019)). For this fixed x we will prove that the problem is always maximised in an EGS.…”

“…This creates an optimisation problem with the enzyme concentrations as the optimisation variables, a problem that is nonlinear when nonlinear enzyme kinetics were introduced. The solution space, and the optimal solutions, can still be understood in terms of EFMs (Wortel et al, 2014;Müller et al, 2014;de Groot et al, 2019).…”

Selecting for lactic acid producing and utilising bacteria in anaerobic enrichment cultures

“…Lactate delivers two ATP by substrate level phosphorylation, while acetate and ethanol deliver three ATP. This switch is thought to be caused by resource allocation, which essentially describes that a cell has a certain amount of functional protein available, and shorter catabolic pathways can evoke a higher biomass specific substrate uptake rate, q s max (de Groot, van Boxtel, Planqué, Bruggeman, & Teusink, 2018;Molenaar, van Berlo, de Ridder, & Teusink, 2009), often at the expense of less energy harvesting per unit of substrate.…”

A natural variant of the sole pyruvate kinase of fission yeast lowers glycolytic flux triggering increased respiration and oxidative-stress resistance but decreased growth

“…Analogously, human cancer cells typically grow by aerobic glycolysis, known as the Warburg effect 10 , thought to increase biosynthetic capacity [11][12][13] . Proposed explanations for how aerobic glycolysis allows faster proliferation involve efficient resource allocation 14,15 and molecular crowding [16][17][18][19] , among others [20][21][22] .…”